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Universalium. 2010.
Heine–Borel theorem — In the topology of metric spaces the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states:For a subset S of Euclidean space R n , the following two statements are equivalent: * S is closed and bounded *every open cover of S has a … Wikipedia
Heine-Borel theorem — /huy neuh baw rel , beuh /, Math. the theorem that in a metric space every covering consisting of open sets that covers a closed and compact set has a finite collection of subsets that covers the given set. Also called Borel Lebesque theorem.… … Useful english dictionary
Borel-Lebesgue theorem — /baw rel leuh beg , beuh /, Math. See Heine Borel theorem. [1950 55; named after F.E.E. BOREL and H. LEBESGUE] * * * … Universalium
Borel-Lebesgue theorem — /baw rel leuh beg , beuh /, Math. See Heine Borel theorem. [1950 55; named after F.E.E. BOREL and H. LEBESGUE] … Useful english dictionary
Bolzano–Weierstrass theorem — In real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite dimensional Euclidean space R^n. The theorem states that each bounded sequence in R^n has a convergent subsequence. An equivalent formulation… … Wikipedia
Émile Borel — Infobox Person name = Félix Édouard Justin Émile Borel image size = 200px caption = Émile Borel birth date = birth date|1871|1|7|mf=y birth place = Saint Affrique, France death date = death date and age|1956|2|3|1871|1|7|mf=y death place = Paris … Wikipedia
Cousin's theorem — In real analysis, a branch of mathematics, Cousin s theorem states that: If for every point of a closed region (in modern terms, closed and bounded ) there is a circle of finite radius (in modern term, a neighborhood ) , then the region can be… … Wikipedia
Eduard Heine — Heinrich Eduard Heine (March 15 1821 ndash;October 21, 1881) was a German mathematician.Heine was born in Berlin, and became known for results on special functions and in real analysis. In particular, he authored an important treatise on… … Wikipedia
Kakutani fixed point theorem — In mathematical analysis, the Kakutani fixed point theorem is a fixed point theorem for set valued functions. It provides sufficient conditions for a set valued function defined on a convex, compact subset of a Euclidean space to have a fixed… … Wikipedia
Regularity theorem for Lebesgue measure — In mathematics, the regularity theorem for Lebesgue measure is a result in measure theory that states that Lebesgue measure on the real line is a regular measure. Informally speaking, this means that every Lebesgue measurable subset of the real… … Wikipedia
